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Proof step 82 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), ino ∈ files, ino ∈ icache ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = content0[m, buf][n], datakey(ino, n) = datakey(ino, m), n ∈ content0, datakey(ino, n) ∈ pcache

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 83:
icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino ∈ files ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = content0[m, buf][n], datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache, n ∈ content0, n ∈ mkcontent(ino, pcache)

Rule argument

fma: n ∈ mkcontent(ino, pcache)

Additional information

Used simplifier rules: at-overwrite-content-new: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n];%at-mkcontent: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used formulas: n ∈ mkcontent(ino, pcache)